Because we're optimizing (taking an argmax) with respect to theta for some fixed dataset x, the 1/p(x) is just a constant factor -- p(x) is just some number (an

Because we're optimizing (taking an argmax) with respect to theta for some fixed dataset x, the 1/p(x) is just a constant factor -- p(x) is just some number (and a non-negative one, since it's a probability). It's like saying argmax_{theta} 0.87*f(theta) = argmax_{theta} f(theta).